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Imagine someone who has no children and decides to either save for retirement using a Roth IRA or a traditional 401k exclusively. Could having a child and then receiving the child tax-credit affect whether using ROTH or traditional means is the lowest tax way of saving for retirement?

My intuition is that it won't, since the child tax credit seems pretty independent of anything else. However, I could be getting all of my federal tax money back in child tax credits and using a 401k as a mechanism to defer taxes until later. It seems odd to defer taxes when I'm really not paying any net taxes.

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No. Per definition tax credits do not modify your income for tax, only the amount paid. In other words, they will not modify your Adjusted Gross Income (AGI).

Decisions around Roth and traditional 401K/IRA will all center around AGI. Tax credits are applied "long" after the AGI calculation and either reduced the tax owed, or increase the amount of refund.

Related, but very different is that you could use the tax credit for funding some kind of IRA. You get your tax return, and provided money is deposited prior to Apr 15th, the contribution will count to the previous tax year.

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